RV of Charitable Gift - the right side of the numerator

CFA Level III Portfolio Management
#1

Can somebody explain the right side of the numerator of the RV of Charitable Gratuitous Transfers.

RV Char. Gift=(1+rg)n+Toi[1+re(1−tie)]^n(1−Te) / [1+re(1−tie)]^n(1−Te)

I understand that this is due to the exempt from paying tax on income/investment return, but 1. why is used investment return already transferred to charity? 2. Why the investment return is multiplied by tax on ordinary income? and 3. why is not consider other income (from employment …)?

#2

Because Gratuitous transfer was made, you earned a savings of Toi.

This is essentially being compounded as though funds available to you to grow at [1+re(1−tie)]^n

You can think of it as being put back into the estate - and earning the returns that the estate earns (1+re (1-Tie))^n

(And this is being compared to the situation when the gratuitous transfer did not happen).

#3

There are three benefits in giving money to charity:

(1) The gift made to the charity accrues tax free inside the tax-exempt organization = (1 + rg)^n - this is a benefit to the charity

(2) The right side of the equation is the benefit provided to the donor of the gift, notice the equation adds these two benefits to (1) above

  • The gift escapes gift tax - (1- Te)
  • The gift provides the donor with an immediate income tax deduction - this creates value in the estate, Toi is the tax rate on ordinary income and captures the income tax benefit associated with the donation

Volume 2, Study Session 4, Reading 10 Estate Planning in the Global Context, Section 4.6, pgs 298-299 AND BlueBox 7 is a must! Work the numbers in BB7 and you will see the three benefits of giving money away now (Charitable gift) rather than when you die (bequest) and the RV is larger with a gift because (1) charity grows the assets tax free (2) reduce the amount of estate tax had the asset stayed in the estate and been taxed at a high rate (3) donor receives an immediate income tax deduction for the gift.

I hope this helps,

Marc A. LeFebvre, CFa

Founder & President, LevelUp, LLC and LevelUp BootCamps

www.levelupbootcamps.com

#4

But why the second part of the equation in the numerator in relation to reducing the givers tax bill (Toi) - takes into account the future value of the estate as if it has been held by the giver and then subject to the estate tax?

#5
RV_{Charitable Gift} = \frac{\left(1+r_g\right)^n + T_{oi}\left[1 + r_e\left(1 − t_{ie}\right)\right]^n\left(1 − T_e\right)}{\left[1 + r_e\left(1 − t_{ie}\right)\right]^n\left(1 − T_e\right)}

The taxes you save by making a charitable gift will grow at the estate’s investment return rate (net of income taxes), then will be donated to the charity (net of estate tax).